Variations of a class of Monge-Ampère-type functionals and their applications

DOI10.2140/apde.2021.14.689zbMath1468.35047OpenAlexW3160059718MaRDI QIDQ2037451

Haodi Chen, Qi-Rui Li, Shibing Chen

Publication date: 1 July 2021

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/apde.2021.14.689

zbMATH Keywords

stabilitysecond variationMinkowski-type problemsnonuniquenessMonge-Ampère-type functionals

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Variational methods for second-order elliptic equations (35J20) Monge-Ampère equations (35J96)

Related Items (15)

Multiple solutions of the planar \(L_p\) dual Minkowski problem ⋮ A class of inverse curvature flows and 𝐿^{𝑝} dual Christoffel-Minkowski problem ⋮ A flow approach to the Musielak-Orlicz-Gauss image problem ⋮ Smooth solutions to the Gauss image problem ⋮ The \(L_p\) Gauss image problem ⋮ \(L_p\)-curvature measures and \(L_{p, q}\)-mixed volumes ⋮ On the \(L_p\) Gaussian Minkowski problem ⋮ Variational analysis of the planar \(L_p\) dual Minkowski problem ⋮ Convex hypersurfaces with prescribed Musielak-Orlicz-Gauss image measure ⋮ On the uniqueness of solutions to the isotropic \(L_p\) dual Minkowski problem ⋮ Flow by Gauss curvature to the \(L_p\) dual Minkowski problem ⋮ \(C^{1,1}\) regularity for solutions to the degenerate \(L_p\) dual Minkowski problem ⋮ The \(L_p\) dual Minkowski problem and related parabolic flows ⋮ Existence of smooth even solutions to the dual Orlicz-Minkowski problem ⋮ A class of Gauss curvature flows and its applications to an even dual Orlicz-Minkowski type problem

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